Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: olcott Newsgroups: sci.logic,comp.theory Subject: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Date: Sun, 4 May 2025 21:23:56 -0500 Organization: A noiseless patient Spider Lines: 18 Message-ID: MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Mon, 05 May 2025 04:23:58 +0200 (CEST) Injection-Info: dont-email.me; posting-host="0a6320ec149f030cd98ca15e4d2d5e5f"; logging-data="3653830"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+FyV5dvPxkhu1JpfI7I6GI" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:kMNznBJORGqci7VB4NojSfYGRiI= X-Antivirus: Norton (VPS 250504-4, 5/4/2025), Outbound message X-Antivirus-Status: Clean Content-Language: en-US Bytes: 1918 When we define formal systems as a finite list of basic facts and allow semantic logical entailment as the only rule of inference we have systems that can express any truth that can be expressed in language. Also with such systems Undecidability is impossible. The only incompleteness are things that are unknown or unknowable. The language of such a formal system is an extended form of the Montague Grammar of natural language semantics. I came up with this mostly in the last two years. I have been working on it for 22 years. The Montague Grammar Rudolf Carnap Meaning postulates are organized in a knowledge ontology inheritance hierarchy. https://en.wikipedia.org/wiki/Ontology_(information_science) -- Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer